Both 'the' and 'a' can be correct here -- it really depends on what you mean. Please see our Articles 1 and 2 pages for an explanation. Our definite and indefinite articles pages also explain each article in detail.

It's possible to guess whether some nouns are count or uncount. For example, substances which are liquid or similar tend to be uncount, such as coffee, for example. Abstract nouns are also often uncount. However, it is not always obvious and it is really a question of learning this when you learn the word itself, just as you would learn the pronunciation or the spelling. Sometimes a word can be both count or uncount. For example, 'coffee' is uncount when referring to the substance, but we can also say 'two coffees' meaning 'two cups of coffee'.

'Furniture' is not a count noun and we would not use it in the way you suggest. We would say 'pieces of furniture'. However, sometimes language in automatically generated invoices, created by computer programmes, is not completely grammatical and you may have seen an example of this.